PDLACONSB(3) ScaLAPACK routine of NEC Numeric Library Collection PDLACONSB(3)
NAME
PDLACONSB - look for two consecutive small subdiagonal elements by see-
ing the effect of starting a double shift QR iteration given by H44,
H33, & H43H34 and see if this would make a subdiagonal negligible
SYNOPSIS
SUBROUTINE PDLACONSB( A, DESCA, I, L, M, H44, H33, H43H34, BUF, LWORK )
INTEGER I, L, LWORK, M
DOUBLE PRECISION H33, H43H34, H44
INTEGER DESCA( * )
DOUBLE PRECISION A( * ), BUF( * )
PURPOSE
PDLACONSB looks for two consecutive small subdiagonal elements by see-
ing the effect of starting a double shift QR iteration given by H44,
H33, & H43H34 and see if this would make a subdiagonal negligible.
Notes
=====
Each global data object is described by an associated description vec-
tor. This vector stores the information required to establish the map-
ping between an object element and its corresponding process and memory
location.
Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA. In the
following comments, the character _ should be read as "of the global
array".
NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).
Let K be the number of rows or columns of a distributed matrix, and
assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process would
receive if K were distributed over the p processes of its process col-
umn.
Similarly, LOCc( K ) denotes the number of elements of K that a process
would receive if K were distributed over the q processes of its process
row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). An upper
bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
ARGUMENTS
A (global input) DOUBLE PRECISION array, dimension
(DESCA(LLD_),*) On entry, the Hessenberg matrix whose tridiago-
nal part is being scanned. Unchanged on exit.
DESCA (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
I (global input) INTEGER
The global location of the bottom of the unreduced submatrix of
A. Unchanged on exit.
L (global input) INTEGER
The global location of the top of the unreduced submatrix of A.
Unchanged on exit.
M (global output) INTEGER
On exit, this yields the starting location of the QR double
shift. This will satisfy: L <= M <= I-2.
H44 H33 H43H34 (global input) DOUBLE PRECISION These three
values are for the double shift QR iteration.
BUF (local output) DOUBLE PRECISION array of size LWORK.
LWORK (global input) INTEGER
On exit, LWORK is the size of the work buffer. This must be at
least 7*Ceil( Ceil( (I-L)/HBL ) / LCM(NPROW,NPCOL) ) Here LCM
is least common multiple, and NPROWxNPCOL is the logical grid
size.
Logic:
======
Two consecutive small subdiagonal elements will stall conver-
gence of a double shift if their product is small relatively
even if each is not very small. Thus it is necessary to scan
the "tridiagonal portion of the matrix." In the LAPACK algo-
rithm DLAHQR, a loop of M goes from I-2 down to L and examines
H(m,m),H(m+1,m+1),H(m+1,m),H(m,m+1),H(m-1,m-1),H(m,m-1), and
H(m+2,m-1). Since these elements may be on separate proces-
sors, the first major loop (10) goes over the tridiagonal and
has each node store whatever values of the 7 it has that the
node owning H(m,m) does not. This will occur on a border and
can happen in no more than 3 locations per block assuming
square blocks. There are 5 buffers that each node stores these
values: a buffer to send diagonally down and right, a buffer
to send up, a buffer to send left, a buffer to send diagonally
up and left and a buffer to send right. Each of these buffers
is actually stored in one buffer BUF where BUF(ISTR1+1) starts
the first buffer, BUF(ISTR2+1) starts the second, etc.. After
the values are stored, if there are any values that a node
needs, they will be sent and received. Then the next major
loop passes over the data and searches for two consecutive
small subdiagonals.
Notes:
======
This routine does a global maximum and must be called by all
processes.
Implemented by: G. Henry, November 17, 1996
ScaLAPACK routine 31 October 2017 PDLACONSB(3)